The spectral excess theorem for graphs with few eigenvalues whose distance- 2 or distance-1-or-2 graph is strongly regular

We study regular graphs whose distance-2 graph or distance-1-or-2 graph is strongly regular. We provide a characterization of such graphs Γ (among regular graphs with few distinct eigenvalues) in terms of the spectrum and the mean number of vertices at maximal distance d from every vertex, where d+1...

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Detalles Bibliográficos
Autores: Dalfó, Cristina, Fiol Mora, Miguel Ángel, Koolen, Jack
Tipo de recurso: artículo
Estado:Versión aceptada para publicación
Fecha de publicación:2018
País:España
Institución:Varias* (Consorci de Biblioteques Universitáries de Catalunya, Centre de Serveis Científics i Acadèmics de Catalunya)
Repositorio:Recercat. Dipósit de la Recerca de Catalunya
OAI Identifier:oai:recercat.cat:10459.1/67511
Acceso en línea:https://doi.org/10.1080/03081087.2018.1491944
http://hdl.handle.net/10459.1/67511
Access Level:acceso abierto
Palabra clave:Distance-regular graph
Distance-2 graph
Spectrum
Predistance polynomials
Descripción
Sumario:We study regular graphs whose distance-2 graph or distance-1-or-2 graph is strongly regular. We provide a characterization of such graphs Γ (among regular graphs with few distinct eigenvalues) in terms of the spectrum and the mean number of vertices at maximal distance d from every vertex, where d+1 is the number of different eigenvalues of Γ. This can be seen as another version of the so-called spectral excess theorem, which characterizes in a similar way those regular graphs that are distance-regular.